Query Processing

1. Query Processing • A query is stated using SQL or other languages, ideally natural languages • After query parsing, each query is essentially treated as a relational algebra expression • Query optimizer • Enumerates the possible plans to evaluate expression, • Select a small subset of these plans and estimate their cost User Query Query Parser Parsed Query Query Optimizer Catalog Manager Plan Generator Plan Cost Estimator Query Plan Evaluator

2. Relational Algebra • Basic relation operators: • Selection ( ): Selects a subset of rows from relation. • Projection ( ): Selects a subset of columns from relation. • Traditional set operators • Union ( ) : combine tuples in R1 and in R2 • Intersection ( ) : tuples in both R1 and R2 • Difference ( ): Tuples in R1, but not in R2. • Cross-product ( ): “Multiplex” two relations

3. S1 • PROJECT implicitly removes any duplicate tuples. • Duplicate elimination is necessary to ensure that the result of the PROJECT is also a relation.

4. Join The result of the join operation between two operand relations R and S is a relation that has one tuple for each combination of tuples – one from R and one from S – whenever the combination satisfies the join condition. R1 S1

5. Two Special Types of Joins • Equi-Join: A special case of condition join where the condition c contains only equalities. • Result schemasimilar to cross-product, but only one copy of fields for which equality is specified is retained. • Natural Join: Equijoin on all common fields

6. A parsed query is essentially treated as an relational algebra expression

7. SQL  Relational Algebra Expression

8. SQL  Relational Algebra Expression

9. Expressive Power • Given a query language, can it express all the queries that can be expressed by relational algebra? • If yes, the query language is said to be relationally complete • A practical query language should be relationally complete • In fact, it typically needs to support features that allow one to expressed some queries that cannot be expressed in relational algebra

10. User Query parser Relational Algebra Expression Query evaluation processor Query Results

11. Query Evaluation Plan • A plan consists of an extended relational algebra tree • Additional annotations are used to indicated the access and/or implementation method • Plan without indexes • Plan with indexes • etc.

12. sname rating > 5 bid=100 sid=sid Sailors Reserves (On-the-fly) sname (On-the-fly) rating > 5 bid=100 (Simple Nested Loops) sid=sid Sailors Reserves SELECT S.sname FROM Reserves R, Sailors S WHERE R.sid=S.sid AND R.bid=100 AND S.rating>5 Plan: RA Tree:

13. Relational Algebra Equivalences • Allow us to choose different join orders and to `push’ selections and projections ahead of joins. • Selections: (Cascade) (Commute) • Projections: (Cascade) (Associative) • Joins: R (S T) (R S) T (Commute) (R S) (S R) R (S T) (T R) S • Show that:

14. More Equivalences • A projection commutes with a selection that only uses attributes retained by the projection. • Selection between attributes of the two arguments of a cross-product converts cross-product to a join. • A selection on just attributes of R commutes with R S. (i.e., (R S) (R) S ) • Similarly, if a projection follows a join R S, we can `push’ it by retaining only attributes of R (and S) that are needed for the join or are kept by the projection.

15. Overview of Query Optimization • Two main issues: • For a given query, what plans are considered? • How is the cost of a plan estimated? • Ideally: Want to find best plan. • Practically: Avoid worst plans!

16. Query Blocks: Units of Optimization • An SQL query is parsed into a collection of queryblocks, and these are optimized one block at a time. • A query block is an SQL query with no nesting and exactly one SELECT clause and one FROM clause and at most one WHERE clause, etc. • Nested blocks are usually treated as calls to a subroutine, made once per outer tuple. • This is an over-simplification, but serves for now. SELECTS.sname FROM Sailors S WHERES.ageIN (SELECT MAX (S2.age) FROM Sailors S2 GROUP BY S2.rating) Outer block Nested block

17. Highlights of System R Optimizer • Impact: • Most widely used currently; works well for < 10 joins. • Cost estimation: • Statistics, maintained in system catalogs, used to estimate cost of operations and result sizes. • Considers combination of CPU and I/O costs. • Plan Space: • Only the space of left-deep plans is considered. • Left-deep plans allow output of each operator to be pipelinedinto the next operator without storing it in a temporary relation. • Cartesian products avoided.

18. Statistics and Catalogs • Need information about the relations and indexes involved. Catalogstypically contain at least: • # tuples (NTuples) and # pages (NPages) for each relation. • # distinct key values (NKeys) for each index. • Index height, low/high key values (Low/High) for each tree index. • Catalogs updated periodically. • Updating whenever data changes is too expensive; lots of approximation anyway, so slight inconsistency ok. • More detailed information (e.g., histograms of the values in some field) are sometimes stored.

19. Cost Estimation • Given a plan, we need to • estimate costof each operation in plan tree • Use the information recorded in statistics and system catalogs • Depends on input cardinalities. • We’ve already discussed how to estimate the cost of operations (sequential scan, index scan, joins, etc.) • estimate size of result for each operation in tree • Use information about the input relations. • For selections and joins, assume independence of predicates.

20. Size Estimation and Reduction Factors SELECT attribute list FROM relation list WHERE term1 AND ... ANDtermk • Consider a query block: • Maximum # tuples in result is the product of the cardinalities of relations in the FROM clause. • Reduction factor (RF) associated with eachtermreflects the impact of the term in reducing result size. Resultcardinality = Max # tuples * product of all RF’s. • Implicit assumption that terms are independent! • Term col=value has RF 1/NKeys(I), given index I on col • Term col1=col2 has RF 1/MAX(NKeys(I1), NKeys(I2)) • Termcol>value has RF (High(I)-value)/(High(I)-Low(I))

21. D D C C D B A C B A B A Plans to consider • Fundamental decision in System R: only left-deep join treesare considered. • As the number of joins increases, the number of alternative plans grows rapidly; we need to restrict the search space. • Left-deep trees allow us to generate all fully pipelined plans. • Intermediate results not written to temporary files.

22. Enumeration of Left-Deep Plans • Left-deep plans differ only in the order of relations, the access method for each relation, and the join method for each join. • Enumerated using N passes (if N relations joined): • Pass 1: Find best 1-relation plan for each relation. • Pass 2: Find best way to join result of each 1-relation plan (as outer) to another relation. (All 2-relation plans.) • Pass N: Find best way to join result of a (N-1)-relation plan (as outer) to the N’th relation. (All N-relation plans.) • For each subset of relations, retain only: • Cheapest plan overall, plus • Cheapest plan for each interesting order of the tuples. • In spite of pruning plan space, this approach is still exponential. N relations imply N! left deep tree ordering.

23. Enumeration of Plans (Contd.) • ORDER BY, GROUP BY, aggregates etc. handled as a final step, using either an `interestingly ordered’ plan or an additional sorting operator. • An N-1 way plan is not combined with an additional relation unless there is a join condition between them, unless all predicates in WHERE have been used up. • i.e., avoid Cartesian products if possible.

24. Summary • Two parts to optimizing a query: • Consider a set of alternative plans, typically, left-deep plans only. • Must estimate cost of each plan that is considered. • Must estimate size of result and cost for each plan node. • Key issues: Statistics, indexes, operator implementations. • Single-relation queries: • All access paths considered, cheapest is chosen. • Issues: Selections that match index, whether index key has all needed fields and/or provides tuples in a desired order. • Multiple-relation queries: • All single-relation plans are first enumerated • Selections/projections considered as early as possible. • For each 1-relation plan, all ways of joining another relation are considered. • For each 2-relation plan that is `retained’, all ways of joining another relation are considered, etc.